Related papers: HYPERgeometric functions DIfferential REduction: M…
In this article we derive differential recursion relations for the Laguerre functions on the cone C of positive definite real matrices. The highest weight representations of the group Sp(n,R) play a fundamental role. Each such…
It is known that a large class of integrable hydrodynamic type systems can be constructed through the Lauricella function, a generalization of the classical Gauss hypergeometric function. In this paper, we construct novel class of…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct new summation formulas…
This paper presents a somewhat exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric equation (CFGHE) about the fractional regular singular…
In many applications (hupergeometric-type) special functions like orthogonal polynomials are needed. For example in more than 50% of the published solutions for the (application-oriented) questions in the "Problems Section" of SIAM Review…
In conventional federated hyperdimensional computing (HDC), training larger models usually results in higher predictive performance but also requires more computational, communication, and energy resources. If the system resources are…
We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable…
Simulated high-dimensional data is useful for testing, validating, and improving algorithms used in dimension reduction, supervised and unsupervised learning. High-dimensional data is characterized by multiple variables that are dependent…
We are going to study properties of "hypergeometrization" -- an operator which act on analytic functions near the origin by inserting two Pochhammer symbols into their Taylor series. In essence, this operator maps elementary function into…
Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables $z_i$, we derive a system of partial differential equations w.r.t.\ new variables $x_j$, which parameterize the…
We obtain the asymptotic expansion for the Gauss hypergeometric function \[F(a-\lambda,b+\lambda;c+i\alpha\lambda;z)\] for $\lambda\rightarrow+\infty$ with $a$, $b$ and $c$ finite parameters by application of the method of steepest…
Hierarchical Model reduction and Proper Generalized Decomposition both exploit separation of variables to perform a model reduction. After setting the basics, we exemplify these techniques on some standard elliptic problems to highlight…
The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, particularly in the context of nonsmooth optimization. The present work proposes…
A series of problems in different fields such as physics and chemistry are modeled by differential equations. Differential equations are divided into partial differential equations and ordinary differential equations which can be linear or…
This article gives a classification scheme of algebraic transformations of Gauss hypergeometric functions, or pull-back transformations between hypergeometric differential equations. The classification recovers the classical transformations…
Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…
We derive an explicit c-function expansion of a basic hypergeometric function associated to root systems. The basic hypergeometric function in question was constructed as explicit series expansion in symmetric Macdonald polynomials by…
The generalized Fermi-Dirac functions and their derivatives are important in evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized Fermi-Dirac…
This paper presents explicit algebraic transformations of some Gauss hypergeometric functions. Specifically, the transformations considered apply to hypergeometric solutions of hypergeometric differential equations with the local exponent…